Stability in terms of two measures for impulsive differential equations with ``supremum''

Sufficient conditions for stability in terms of two measures for nonlinear impulsive differential equations with ``supremum'' are obtained. Perturbing piecewise continuous Lyapunov functions have been applied. Razumikhin method and comparison scalar impulsive ordinary differential equations have been employed. The obtained sufficient conditions significantly depend on the impulses.

[1]  On the asymptotic stability of differential equations with “maxima” , 1991 .

[2]  Xinyu Song,et al.  Strict practical stability of nonlinear impulsive systems by employing two Lyapunov-like functions , 2008 .

[3]  V. Lakshmikantham,et al.  Practical Stability Of Nonlinear Systems , 1990 .

[4]  Peiguang Wang,et al.  Practical stability of impulsive hybrid differential systems in terms of two measures on time scales , 2006 .

[5]  V. G. Angelov,et al.  ON THE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH "MAXIMUMS" , 1983 .

[6]  Guisheng Zhai,et al.  Practical stability and stabilization of hybrid and switched systems , 2004, IEEE Trans. Autom. Control..

[7]  Snezhana Hristova,et al.  Differential Equations with Maxima , 2011 .

[8]  Weining Feng.  On practical stability of linear multivariable feedback systems with time-delays , 1991, Autom..

[9]  Leon O. Chua,et al.  Practical stability of impulsive Synchronization between Two nonautonomous Chaotic Systems , 2000, Int. J. Bifurc. Chaos.

[10]  Johnny Henderson,et al.  EVENTUAL PRACTICAL STABILITY AND CONE VALUED LYAPUNOV FUNCTIONS FOR DIFFERENTIAL EQUATIONS WITH “MAXIMA” , 2010 .

[11]  E. Stepanov.  On solvability of some boundary value problems for differential equations with "maxima" , 1996 .

[12]  Xinzhi Liu,et al.  Practical Stability of Impulsive Delay Differential Equations and Applications to Control Problems , 2001 .

[13]  Yang Liu,et al.  A new approach to practical stability of impulsive functional differential equations in terms of two measures , 2009 .

[14]  Yu Zhang,et al.  Practical stability of impulsive functional differential equations in terms of two measurements , 2004 .

[15]  V. I. Slyn’ko.  Sufficient practical-stability conditions for nonlinear impulsive systems , 2004 .

[16]  Guoping Chen,et al.  Practical stability of impulsive functional differential equations , 2009 .

[17]  An Li,et al.  Practical stability of nonlinear differential equation with initial time difference , 2008, Appl. Math. Comput..

[18]  Yu Zhang,et al.  Eventual practical stability of impulsive differential equations with time delay in terms of two measurements , 2005 .

[19]  S. Hristova.  LIPSCHITZ STABILITY FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH “ SUPREMUM ” , 2010 .

[20]  D. Bainov,et al.  On the functional differential equations with “maximums” , 1987 .

[21]  V. Lakshmikantham,et al.  Stability Analysis in Terms of Two Measures , 1993 .